Cap 23 - Ótica Geométrica

Ótica Geométrica

Descreve o comportamento da luz em situações onde sua natureza ondulatória (efeitos de interferência/difração) não fica evidente, e onde ela pode ser modelada por meio de

raios de luz

Os raios de luz definem a direção na qual a energia flui.

Ótica Geométrica

Na prática: deve ser utilizada sempre que as aberturas/obstáculos no caminho da luz são muito maiores que o comprimento de onda

Ótica Geométrica Ótica Ondulatória

Ex: p/ λ=500nm, se a luz passa por aberturas de tamanho D<~1mm, devemos usar a ótica ondulatória, caso contrário, podemos utilizar a ótica geométrica.

Ótica Geométrica

Princípios: 1 - Propagação retilínea da luz com velocidade v = c / n (em meios homogêneos, transparentes e isotrópicos)

Teste conceitual

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Tela

Uma lâmpada pontual (muito pequena) ilumina uma abertura vertical com 1cm de largura. Qual é o formato do padrão luminoso projetado em uma tela atrás da abertura?

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Lâmpada

Tela

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Teste conceitual

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Tela Uma lâmpada pontual (muito pequena) ilumina uma abertura vertical com 1cm de largura. Qual é o formato do padrão luminoso projetado em uma tela atrás da abertura?

Lâmpada

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Teste conceitual

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Lâmpada

Uma lâmpada horizontal longa e fina ilumina uma abertura vertical com 1cm de largura. Qual é o formato do padrão luminoso projetado em uma tela atrás da abertura?

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Tela

Lâmpada

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Lâmpada

Teste conceitual

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Uma lâmpada horizontal longa e fina ilumina uma abertura vertical com 1cm de largura. Qual é o formato do padrão luminoso projetado em uma tela atrás da abertura?

658 c h a p t e r 23 . Ray Optics

You can see from the similar triangles in Figure 23.5b that the object and image heights are related by

hi

ho=

di

do (23.1)

where do is the distance to the object and di is the depth of the camera obscura. Any realistic camera obscura has di 6 do; thus the image is smaller than the object.

We can apply the ray model to more complex apertures, such as the L-shaped aper-ture in FIGURE 23.6. The pattern of light on the screen is found by tracing all the straight-line paths—the ray trajectories—that start from the point source and pass through the aperture. We will see an enlarged L on the screen, with a sharp boundary between the image and the dark shadow.

STOP TO THINK 23.1 A long, thin lightbulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture?

23.2 ReflectionReflection of light is a familiar, everyday experience. You see your reflection in the bathroom mirror first thing every morning, reflections in your car’s rearview mirror as you drive to school, and the sky reflected in puddles of standing water. Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection, from speculum, the Latin word for “mirror.”

FIGURE 23.7a shows a bundle of parallel light rays reflecting from a mirror-like sur-face. You can see that the incident and reflected rays are both in a plane that is normal, or perpendicular, to the reflective surface. A three-dimensional perspective accurately shows the relationship between the light rays and the surface, but figures such as this are hard to draw by hand. Instead, it is customary to represent reflection with the sim-pler pictorial representation of FIGURE 23.7b. In this figure,

■ The plane of the page is the plane of incidence, the plane containing both incident and reflected rays. The reflective surface extends into the page.

■ A single light ray represents the entire bundle of parallel rays. This is oversimpli-fied, but it keeps the figure and the analysis clear.

The angle ui between the ray and a line perpendicular to the surface—the normal to the surface—is called the angle of incidence. Similarly, the angle of reflection ur is the angle between the reflected ray and the normal to the surface. The law of reflec-tion, easily demonstrated with simple experiments, states that

1. The incident ray and the reflected ray are in the same plane normal to the sur-face, and

2. The angle of reflection equals the angle of incidence: ur = ui.

NOTE ! Optics calculations always use the angle measured from the normal, not the angle between the ray and the surface. "

Some rays areblocked by theopaque screen.

Light

Point source

Aperture

Screen

Shadow

FIGURE 23.6 Light through an aperture.

(a)

Light

Screen

(b) (c) (d)(a)

Light

Screen

(a)

(b)

Angle ofincidence

Normal

Reflective surface

ui ur

Angle ofreflection

Reflected rayIncident ray

Reflectivesurface

The incident and reflected rays liein the plane of incidence, a planeperpendicular to the surface.

FIGURE 23.7 Specular reflection of light.

Tela

Ótica Geométrica

Princípios: 1 - Propagação retilínea (raios de luz) 2 - Independência dos raios luminosos (um raio não afeta o outro)

(isto é uma consequencia do pricípio da superposição das onda subjacentes)

Ótica Geométrica

Princípios: 1 - Propagação retilínea (raios de luz) 2 - Independência dos raios luminosos (um raio não afeta o outro) 3- Cada ponto de um objeto físico origina raios de luz, e esses

raios se propagam em todas as direções

656 c h a p t e r 23 . Ray Optics

23.1 The Ray Model of LightA flashlight makes a beam of light through the night’s darkness. Sunbeams stream into a darkened room through a small hole in the shade. Laser beams are even more well defined. Our everyday experience that light travels in straight lines is the basis of the ray model of light.

The ray model is an oversimplification of reality but nonetheless is very useful within its range of validity. In particular, the ray model of light is valid as long as any apertures through which the light passes (lenses, mirrors, and holes) are very large compared to the wavelength of light. In that case, diffraction and other wave aspects of light are negligible and can be ignored. The analysis of Section 22.5 found that the crossover between wave optics and ray optics occurs for apertures ! 1 mm in diam-eter. Lenses and mirrors are almost always larger than 1 mm, so the ray model of light is an excellent basis for the practical optics of image formation.

To begin, let us define a light ray as a line in the direction along which light energy is flowing. A light ray is an abstract idea, not a physical entity or a “thing.” Any nar-row beam of light, such as the laser beam in FIGURE 23.1, is actually a bundle of many parallel light rays. You can think of a single light ray as the limiting case of a laser beam whose diameter approaches zero. Laser beams are good approximations of light rays, certainly adequate for demonstrating ray behavior, but any real laser beam is a bundle of many parallel rays.

The following table outlines five basic ideas and assumptions of the ray model of light.

Light rays

A beam of light

Directionof travel

FIGURE 23.1 A laser beam or beam of sunlight is a bundle of parallel light rays.

The ray model of light

Light rays travel in straight lines.

Light travels through a transparent material in straight lines called light rays. The speed of light is v = c/n, where n is the index of refraction of the material.

Light rays can cross.

Light rays do not interact with each other. Two rays can cross without either being affected in any way.

A light ray travels forever unless it interacts with matter.

A light ray continues forever unless it has an interaction with matter that causes the ray to change direction or to be absorbed. Light interacts with matter in four different ways: ■ At an interface between two materials, light can be either reflected or refracted. ■ Within a material, light can be either scattered or absorbed.

These interactions are discussed later in the chapter.

An object is a source of light rays.

An object is a source of light rays. Rays originate from every point on the object, and each point sends rays in all directions. We make no distinction between self-luminous objects and reflective objects.

The eye sees by focusing a diverging bundle of rays.

The eye “sees” an object when diverging bundles of rays from each point on the object enter the pupil and are focused to an image on the retina. (Imaging is discussed later in the chapter.) From the movements the eye’s lens has to make to focus the image, your brain determines the point from which the rays originated, and you perceive the object as being at that point.

Material 1

ReflectionRefraction

AbsorptionScattering

Material 2

Eye

Diverging bundle of rays

Obs: Isso vale tanto para objetos luminosos (geram luz própria), quanto para os não-luminosos (apenas refletem luz já no ambiente)

Ótica Geométrica

Cada ponto de um objeto é uma fonte de luz Aplicação: Câmara Escura

Ótica Geométrica

Princípios: 1 - Propagação retilínea (raios de luz) 2 - Independência dos raios luminosos (um raio não afeta o outro) 3 - Cada ponto de um objeto físico origina raios de luz, e esses

raios se propagam em todas as direções

4 - Os raios podem ser desviados (refletidos, refratados, ou espalhados) ao interagirem com objetos materiais

Reflexão e Refração da Luz

Raios de luz são desviados quando encontram meios materiais com diferentes indices de refração

N: normal à superfície ; θi = ângulo de incidência ; θr = ângulo de refração

obs: Ângulos sempre contados com respeito à normal N

θ

θ

Os raios incidente, refletido e refratado estão contidos no plano formado pelo raio incidente e a normal.

Numa reflexão especular (=‘tipo espelho’): θi = θrefl Numa refração: ni senθi = nr senθr (Lei de Snell)

Leis da Ótica Geométrica

θrefl θ

θ

Reflexão Especular Reflexão Difusa

obs: O que considerar como ‘irregular’ depende do λluz.

Se a rugosidade for ≳ λluz (para luz visível, ~ 500nm), a reflexão será difusa.

Reflexão

Formação de Imagens em Espelhos planos

O observador vê a luz como se ela viesse de um ponto atrás do espelho. Atrás do espelho não existe objeto algum, por isso

dizemos que a imagem é virtual.

→ Imagem Virtual: Imagem formada por prolongamentos

Reflexão em espelhos planos

Formação de Imagens em Espelhos planos

A distância do objeto ao espelho é igual à da imagem ao espelho

Reflexão em espelhos planos

Formação de Imagens em Espelhos planos

O Objeto e a Imagem têm o mesmo tamanho!!

Reflexão em espelhos planos

Lei de Snell para Refração da Luz

meio 1

meio 2

(n1)

(n2)

Refração

Quem é maior: n1 ou n2?

A) n1 B) n2

Lei de Snell para Refração da Luz

meio 1

meio 2

(n1)

(n2)

Refração

Quem é maior: n1 ou n2?

A) n1 B) n2

R (visão ondulatória): λ1 > λ2 . Mas λ = v/f = c/nf, e f tem de ser o mesmo nos dois lados. Então n1 < n2 .

R: (visão geométrica): n1 / n2 = sen ( θ2 ) / sen ( θ1 ) < 1

Refração: Lei de Snell

n1senθ1 = n2senθ2

l senθ1 = λ1 = (c / n1) / f

c / l f = n1senθ1 = n2senθ2

l senθ2 = λ2 = (c / n2) / f

Reflexão Interna Total

n1senθ1 = n2senθr

Se n2 < n1 e θ1 for suficientemente grande, não há solução para θr

θc=arcsen(n2/n1)

angulo crítico:

θc=arcsen(n2/n1)

θc

n1 > n2

Meio 1 (+ refringente)

Meio 2 (- refringente)

Reflexão Interna Total

Reflexão Interna Total

Aplicação tecnológica:

fibras Óticas Binóculos

Dispersão

Dispersão da luz: Dependência do n com λ

668 c h a p t e r 23 . Ray Optics

to electromagnetic waves of this wavelength. There is no “redness” associated with the light wave itself.

Most of the results of optics do not depend on color. We generally don’t need to know the color of light—or, to be more precise, its wavelength—to use the laws of reflection and refraction. Nonetheless, color is an interesting subject, one worthy of a short digression.

ColorIt has been known since antiquity that irregularly shaped glass and crystals cause sun-light to be broken into various colors. A common idea was that the glass or crystal somehow altered the properties of the light by adding color to the light. Newton sug-gested a different explanation. He first passed a sunbeam through a prism, producing the familiar rainbow of light. We say that the prism disperses the light. Newton’s novel idea, shown in FIGURE 23.27a, was to use a second prism, inverted with respect to the first, to “reassemble” the colors. He found that the light emerging from the second prism was a beam of pure, white light.

But the emerging light beam is white only if all the rays are allowed to move be-tween the two prisms. Blocking some of the rays with small obstacles, as in FIGURE 23.27b, causes the emerging light beam to have color. This suggests that color is associated with the light itself, not with anything that the prism is “doing” to the light. Newton tested this idea by inserting a small aperture between the prisms to pass only the rays of a particular color, such as green. If the prism alters the properties of light, then the second prism should change the green light to other colors. Instead, the light emerging from the second prism is unchanged from the green light entering the prism.

These and similar experiments show that

1. What we perceive as white light is a mixture of all colors. White light can be dispersed into its various colors and, equally important, mixing all the colors produces white light.

2. The index of refraction of a transparent material differs slightly for different colors of light. Glass has a slightly larger index of refraction for violet light than for green light or red light. Consequently, different colors of light refract at slightly different angles. A prism does not alter the light or add anything to the light; it simply causes the different colors that are inherent in white light to follow slightly different trajectories.

DispersionIt was Thomas Young, with his two-slit interference experiment, who showed that different colors are associated with light of different wavelengths. The longest wave-lengths are perceived as red light and the shortest as violet light. Table 23.2 is a brief summary of the visible spectrum of light. Visible-light wavelengths are used so fre-quently that it is well worth committing this short table to memory.

The slight variation of index of refraction with wavelength is known as dispersion. FIGURE 23.28 shows the dispersion curves of two common glasses. Notice that n is larger when the wavelength is shorter, thus violet light refracts more than red light.

FIGURE 23.27 Newton used prisms to study color.

Whitelight

Whitelight

A second prism cancombine the colorsback into white light.

A prism disperseswhite light into colors.

(a)

Whitelight

Greenlight

The second prism doesnot change pure colors.

An aperture selectsa green ray of light.

(b)

TABLE 23.2 A brief summary of the visible spectrum of light

ColorApproximate wavelength

Deepest red 700 nmRed 650 nmGreen 550 nmBlue 450 nmDeepest violet 400 nm

FIGURE 23.28 Dispersion curves show how the index of refraction varies with wavelength.

1.621.601.581.561.541.521.50 l (nm)

300 400 500 600 700 800

Crown glass

UV

IR

Flint glass

n increases as l decreases.n

VISUALIZE Figure 23.19 showed the geometry. A ray of any wave-length is incident on the hypotenuse of the prism at u1 = 30!.

SOLVE a. If n1 = 1.54 for deep red light, the refraction angle is

u2 = sin-11n1 sin u1

n22 = sin-111.54 sin 30!

1.00 2 = 50.4!

EXAMPLE 23.7 Dispersing light with a prismExample 23.4 found that a ray incident on a 30! prism is deflected by 22.6! if the prism’s index of refraction is 1.59. Suppose this is the index of refraction of deep violet light and deep red light has an index of refraction of 1.54.

a. What is the deflection angle for deep red light? b. If a beam of white light is dispersed by this prism, how wide is

the rainbow spectrum on a screen 2.0 m away?

Dispersão

Dispersão da luz: Dependência do n com λ Ex: em vidros, tipicamente n diminui com λ

Quanto maior λ, menor o n → menos a luz é refratada.

By DrBob at the English language Wikipedia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=15170853

O Arco- íris

vermelho acima, violeta abaixo

O Arco- íris

O Arco- íris

Arco principal vermelho acima, violeta abaixo

Arco secundário violeta acima, vermelho abaixo mais fraco

O Arco- íris

Arco secundário: uma reflexão interna a mais!

Formação de imagens através de lentes

Lente: um material transparente que usa a refração em superfícies curvas para a formação de imagens.

Lente ‘convergente’ (convexa) Lente ‘divergente’ (côncava)

23.6 . Thin Lenses: Ray Tracing 671

FIGURE 23.33 shows parallel light rays entering two different lenses. The left lens, called a converging lens, causes the rays to refract toward the optical axis. The com-mon point through which initially parallel rays pass is called the focal point of the lens. The distance of the focal point from the lens is called the focal length f of the lens. The right lens, called a diverging lens, refracts parallel rays away from the opti-cal axis. This lens also has a focal point, but it is not as obvious.

NOTE ! A converging lens is thicker in the center than at the edges. A diverging lens is thicker at the edges than at the center. "

FIGURE 23.34 clarifies the situation. In the case of a diverging lens, a backward projec-tion of the diverging rays shows that they appear to have started from the same point. This is the focal point of a diverging lens, and its distance from the lens is the focal length of the lens. In the next section we’ll relate the focal length to the curvature and index of refraction of the lens, but now we’ll use the practical definition that the fo-cal length is the distance from the lens at which rays parallel to the optical axis converge or from which they diverge.

NOTE ! The focal length f is a property of the lens, independent of how the lens is used. The focal length characterizes a lens in much the same way that a mass m characterizes an object or a spring constant k characterizes a spring. "

Converging LensesThese basic observations about lenses are enough to understand image formation by a thin lens. A thin lens is a lens whose thickness is very small in comparison to its focal length and in comparison to the object and image distances. We’ll make the approximation that the thickness of a thin lens is zero and that the lens lies in a plane called the lens plane. Within this approximation, all refraction occurs as the rays cross the lens plane, and all distances are measured from the lens plane. Fortunately, the thin-lens approximation is quite good for most practical applica-tions of lenses.

NOTE ! We’ll draw lenses as if they have a thickness, because that is how we expect lenses to look, but our analysis will not depend on the shape or thickness of a lens. "

FIGURE 23.35 shows three important situations of light rays passing through a thin converging lens. Part a is familiar from Figure 23.34. If the direction of each of the rays in FIGURE 23.35a is reversed, Snell’s law tells us that each ray will exactly retrace its path and emerge from the lens parallel to the optical axis. This leads to FIGURE 23.35b, which is the “mirror image” of part (a). Notice that the lens actually has two focal points, located at distances f on either side of the lens.

FIGURE 23.35c shows three rays passing through the center of the lens. At the center, the two sides of a lens are very nearly parallel to each other. Earlier, in Example 23.3, we found that a ray passing through a piece of glass with parallel sides is displaced

Converging lens Diverging lens

FIGURE 23.33 Parallel light rays pass through a converging lens and a diverging lens.

Diverging lens

Focal length f

This is the focal point.Rays appear to divergefrom this point.

Parallel rays

Optical axis

This is the focal point.Rays actually convergeat this point.

Converging lens

Parallel rays

Focal length f

Optical axis

FIGURE 23.34 The focal lengths of converging and diverging lenses.

Parallel rays

Far focal point

Lens plane

f

Any ray initially parallel to the opticalaxis will refract through the focal pointon the far side of the lens.

(a)

Parallel rays

Near focal point

f

Any ray passing through the near focalpoint emerges from the lens parallel tothe optical axis.

(b) Lens plane

Center of lensRays arenot bent.

Any ray directed at the center of the lenspasses through in a straight line.

(c)

FIGURE 23.35 Three important sets of rays passing through a thin converging lens.

Ótica Geométrica

Feixe divergente de raios partindo de um mesmo ponto do objeto

Feixe divergente de raios partindo de um mesmo ponto do objeto

Imagem na retina

Como o olho enxerga (rascunho):

Olho

Reflexão em espelhos planos

Imagem por refração: peixe num aquario

s0 =n2

n1sp/ angulos pequenos:

Refração por uma placa de lados paralelos

após atravessar, o feixe continua na mesma direção original, porém com um pequeno deslocamento lateral

d = l sen(✓1 � ✓2) = tsen(✓1 � ✓2)

cos(✓2)

Formação de imagens através de lentes

Lente: um material transparente que usa a refração em superfícies curvas para a formação de imagens.

Lente ‘convergente’ (convexa) Lente ‘divergente’ (côncava)

Formação de imagens através de lentes

Análise: suposições simplificadoras

Assumimos: 1.  lentes finas, que podemos considerar

contidas em um plano 2.  que próximo ao centro da lente as suas

faces são praticamente paralelas.

Consequencias: -  refração ocorre apenas no plano da lente

-  raios que passam pelo centro da lente seguem sem desvio de trajetória,

Formação de imagens através de lentes

Método de traçado de raios

Para determinar graficamente como será a imagem produzida por uma lente convergente

1. Desenhe o eixo óptico com a lente centrada sobre ele

2. Desenhe um objeto vertical a uma distância s à esquerda da lente

3. A partir da ponta superior do objeto, trace os três raios principais: a. um raio incidindo paralelo ao eixo óptico, o qual será refratado de modo a

passar pelo foco distante (direito) b. um raio que passa pelo centro da lente sem desvios c. um raio que passa pelo foco próximo (esquerdo), o qual será refratado de

modo a seguir paralelo ao eixo óptico 4. Esses três raios devem se cruzar em um ponto, o qual será a projeção da ponta do objeto no plano imagem

Teste Conceitual

No exemplo acima, a imagem pode ser vista colocando-se uma uma tela localizada no plano que contém P’, Q’ ,R’. E se mudarmos a posição da tela, por exemplo adiantando-a um pouco como na figura?. O que vemos sobre a tela nesse caso?

A)  A mesma imagem, com o mesmo tamanho B)  A mesma imagem, com tamanho menor C)  A mesma imagem, com tamanho maior D)  Um borrão fora de foco

tela

Teste Conceitual

No exemplo acima, a imagem pode ser vista colocando-se uma uma tela localizada no plano que contém P’, Q’ ,R’. E se mudarmos a posição da tela, por exemplo adiantando-a um pouco como na figura?. O que vemos sobre a tela nesse caso?

A)  A mesma imagem, com o mesmo tamanho B)  A mesma imagem, com tamanho menor C)  A mesma imagem, com tamanho maior D)  Um borrão fora de foco

tela

Teste Conceitual

O que acontece com a imagem se tapamos a metade inferior da lente? A)  Aparece apenas a metade de cima do objeto B)  Aparece apenas a metade de baixo do objeto C)  Aparece o objeto inteiro, mas com menos intensidade D)  Aparece o objeto inteiro, mas fora de foco / borrado

Formação de imagens através de lentes

Método de traçado de raios

Por congruência: h / s = h’ / s’ h / h’ = s / s’

Def: aumento linear transversal: m = - s’ / s obs: convenciona-se s’ < 0 se a imagem estiver do mesmo lado da lente que o objeto

Formação de imagens através de lentes

Método de traçado de raios

Teste Conceitual Neste caso podemos dizer que A)  0 < m < 1 B) m > 1 C)  -1 < m < 0 D) m < -1

Def: aumento linear transversal: m = - s’ / s

Formação de imagens através de lentes

Método de traçado de raios

Teste Conceitual Neste caso podemos dizer que A)  0 < m < 1 B) m > 1 C)  -1 < m < 0 D) m < -1

Def: aumento linear transversal: m = - s’ / s

Formação de imagens através de lentes

Imagens virtuais em lentes convergentes

•  Ocorre se objeto entre o foco e a lente

•  Neste caso raios vindos de um mesmo ponto P do objeto não se reencontram, mas se comportam como se divergissem a partir de uma posição P’ (a “imagem virtual” de P), localizada acima e atrás do objeto real

•  A imagem virtual do objeto é maior do que ele (h’ > h)

•  Obs: note que nesse caso os raios divergem, apesar da lente ser ‘convergente’

Formação de imagens através de lentes

Imagens virtuais em lentes convergentes

Teste Conceitual Neste caso podemos dizer que A) 0 < m < 1 B) m > 1 C) -1 < m < 0 D) m < -1

Formação de imagens através de lentes

Imagens virtuais em lentes convergentes

Teste Conceitual Neste caso podemos dizer que A) 0 < m < 1 B) m > 1 C) -1 < m < 0 D) m < -1

Formação de imagens através de lentes

Imagens em lentes divergentes: método do traçado de raios

Formação de imagens através de lentes

Compare esse caso com aquele que vimos anteriormente, onde a interface era plana. No caso atual, um observador externo verá a imagem virtual em um ponto A)  Mais próximo a ele do que pareceria no caso da interface plana B)  Mais distante dele do que pareceria no caso da interface plana C)  Na mesma distância dele que pareceria no caso da interface plana

Imagens em lentes esféricas

Formação de imagens através de lentes

Compare esse caso com aquele que vimos anteriormente, onde a interface era plana. No caso atual, um observador externo verá a imagem virtual em um ponto A)  Mais próximo a ele do que pareceria no caso da interface plana B)  Mais distante dele do que pareceria no caso da interface plana C)  Na mesma distância dele que pareceria no caso da interface plana

θi

θr

θdesvio = θr – θi

θdesvio

≃(n1θi / n2 – θi) = (n1 / n2 – 1)θi

Imagens em lentes esféricas

Formação de imagens através de lentes

Imagens em lentes esféricas

Compare esse caso com aquele que vimos anteriormente, onde a interface era plana. No caso atual, um observador externo verá a imagem virtual em um ponto A)  Mais próximo a ele do que pareceria no caso da interface plana B)  Mais distante dele do que pareceria no caso da interface plana C)  Na mesma distância dele que pareceria no caso da interface plana

θi

θr

θdesvio = θr – θi

θdesvio

≃(n1θi / n2 – θi) = (n1 / n2 – 1)θi

(pois θi é menor → θdesvio é menor)

Formação de imagens através de lentes

Imagens em lentes esféricas

n1

s+

n2

s0=

n2 � n1

R

Para angulos θ1,2 pequenos, é possível deduzir (v/. livro / quadro)

Obs: convenções de sinal

R > 0 se superfície convexa p/ objeto (como acima) < 0 “ “ côncava “ s’ > 0 se imagem real, no lado oposto a P s’ < 0 se imagem virtual, no mesmo lado de P

Formação de imagens através de lentes

Conferindo exemplo anterior

n1

s+

n2

s0=

n2 � n1

R

s’ < 0 pois a imagem é virtual, no mesmo lado de P

p/ superficie esférica: R < 0 pois superfície côncava p/ objeto

p/ superficie plana: R → ∞

n2

s0esf

=n2

s0plano

+n2 � n1

R

> 0, já que R<0 e n2 < n1

s’esf é mais negativo que s’plano

Imagem com sup. esférica está ‘mais para dentro’ do

que com sup. plana

Conclusão

Equações para lentes com 2 superfícies esféricas

1

s1+

n

s01=

n� 1

R1

lado esquerdo da lente lado direito da lente

lembrando que s’1 <0

n

t� s01+

1

s02=

1� n

R2

e R2 <0 tb

Distância focal da lente

1

f= (n� 1)

✓1

R1� 1

R2

◆1

f=

1

s+

1

s0onde

Fazendo s → ∞ os raios incidentes são paralelos e s’ = f. → Portanto f é de fato a distância focal!

Para lentes finas (“delgadas”), t é desprezível ( t < < |s’1 | ). Redefinindo s1 = s, s2’ = s’ vale

Uma lente convexa tem distância focal f. Um objeto é localizado entre f e 2f em relação a uma linha perpendicular ao centro da lente. A imagem formada é localizada em qual distância da lente? A) 2f B) entre f e 2f C) mais distante que 2f D) entre a lente e f

1

f=

1

s+

1

s0

Teste Conceitual

Uma lente convexa tem distância focal f. Um objeto é localizado entre f e 2f em relação a uma linha perpendicular ao centro da lente. A imagem formada é localizada em qual distância da lente? A) 2f B) entre f e 2f C) mais distante que 2f D) entre a lente e f

Teste Conceitual

1

f=

1

s+

1

s0

Equações para lentes delgadas

1

f= (n� 1)

✓1

R1� 1

R2

◆1

f=

1

s+

1

s0onde

As mesmas equações valem para lentes esféricas delgadas de qualquer formato (ie, podendo cada lado ser côncavo ou convexo, com raios iguais

ou diferentes), respeitando essas convenções de sinal:

Uma lente é utilizada para a formação de uma imagem de um objeto que é colocado à sua frente. A) Se a imagem é real, ela deve ser invertida. B) Se a imagem é real, ela deve ser direita. C) Se a imagem é virtual, ela deve ser invertida. D) Se a imagem é virtual, a lente tem que ser divergente.

Teste Conceitual

Uma lente é utilizada para a formação de uma imagem de um objeto que é colocado à sua frente. A) Se a imagem é real, ela deve ser invertida. B) Se a imagem é real, ela deve ser direita. C) Se a imagem é virtual, ela deve ser invertida. D) Se a imagem é virtual, a lente tem que ser divergente.

Teste Conceitual